BPS Vortices with Negative Electric Charge in The Generalized Maxwell-Chern-Simons-Higgs Model (original) (raw)

Electric-dual BPS Vortices in The Generalized Self-dual Maxwell-Chern-Simons-Higgs Model

arXiv (Cornell University), 2021

In this paper we show how to derive the Bogomolny's equations of the generalized self-dual Maxwell-Chern-Simons-Higgs model presented in [1] by using the BPS Lagrangian method with a particular choice of the BPS Lagrangian density. We also show that the identification, potential terms, and Gauss's law constraint can be derived rigorously under the BPS Lagrangian method. In this method, we find that the potential terms are the most general form that could have the BPS vortex solutions. The Gauss's law constraint turns out to be the Euler-Lagrange equations of the BPS Lagrangian density. We also find another BPS vortex solutions by taking other identification between the neutral scalar field and the electric scalar potential field, N = ±A 0 , which is different by a relative sign to the identification in [1], N = ∓A 0. Under this identification, N = ±A 0 , we obtain a slightly different potential terms and Bogomolny's equations compared to the ones in [1]. Furthermore we compute the solutions numerically, with the same configurations as in [1], and find that only the resulting electric field plots differ by sign relative to the results in [1]. Therefore we conclude that these BPS vortices are electric-dual BPS vortices of the ones computed in [1].

Analytical BPS Maxwell-Higgs Vortices

Advances in High Energy Physics, 2014

We have established a prescription for the calculation of analytical vortex solutions in the context of generalized Maxwell-Higgs models whose overall dynamics is controlled by two positive functions of the scalar field, namely f (|φ|) and w (|φ|). We have also determined a natural constraint between these functions and the Higgs potential U (|φ|), allowing the existence of axially symmetric Bogomol'nyi-Prasad-Sommerfield (BPS) solutions possessing finite energy. Furthermore, when the generalizing functions are chosen suitably, the nonstandard BPS equations can be solved exactly. We have studied some examples, comparing them with the usual Abrikosov-Nielsen-Olesen (ANO) solution. The overall conclusion is that the analytical self-dual vortices are well-behaved in all relevant sectors, strongly supporting the generalized models they belong themselves. In particular, our results mimic well-known properties of the usual (numerical) configurations, as localized energy density, while contributing to the understanding of topological solitons and their description by means of analytical methods.

Electrically and magnetically charged vortices in the Chern–Simons–Higgs theory

2009

In this paper, we prove the existence of finite-energy electrically and magnetically charged vortex solutions in the full Chern-Simons-Higgs theory for which both the Maxwell term and Chern-Simons term are present in the Lagrangian density. We consider both Abelian and non-Abelian cases. The solutions are smooth and satisfy natural boundary conditions. Existence is established via a constrained minimization procedure applied on indefinite action functionals. This work settles a long-standing open problem concerning the existence of dually charged vortices in the classical gauge field Higgs model minimally extended to contain a Chern-Simons term.

Some exact BPS solutions for exotic vortices and monopoles

Physics Letters B, 2016

We present several analytical solutions of BPS vortices and monopoles in the generalized Abelian Maxwell-Higgs and Yang-Mills-Higgs theories, respectively. These models have recently been extensively studied and several exact solutions have already been obtained in [1, 2]. In each theory, the dynamics is controlled by the additional two positive scalar-field-dependent functions, f (|φ|) and w(|φ|). For the case of vortices, we work in the ordinary symmetry-breaking Higgs potential, while for the case of monopoles we have the ordinary condition of the Prasad-Sommerfield limit. Our results generalize that of exact solutions found previously. We also present solutions for BPS vortices with higher winding number. These solutions suffer from the condition that w(|φ|) has negative value at some finite range of r, but we argue that since it satisfies the weaker positivevalue conditions then the corresponding energy density is still positive-definite and, thus, they are acceptable BPS solutions.

Comment on vortices in Chern-Simons and Maxwell electrodynamics with Higgs fields

Physics Letters B, 1994

We compare the vortex-like solutions of two different theories in (2 + 1) dimensions. In the first a nonrelativistic field self-interacts through a Chern-Simons gauge connection. It is P and T violating. The second is the standard Maxwell scalar electrodynamics. We show that for specific values of some parameters the same vortex-configurations provide solutions for both theories.

Vortices in generalized Abelian Chern-Simons-Higgs model

arXiv: High Energy Physics - Theory, 2015

We study a generalization of abelian Chern-Simons-Higgs model by introducing nonstandard kinetic terms. We will obtain a generic form of Bogomolnyi equations by minimizing the energy functional of the model. This generic form of Bogomolnyi equations produce an infinity number of soliton solutions. As a particular limit of these generic Bogomolnyi equations, we obtain the Bogomolnyi equations of the abelian Maxwell-Higgs model and the abelian Chern-Simons Higgs model. Finally, novel soliton solutions emerge from these generic Bogomolnyi equations. We analyze these solutions from theoretical and numerical point of view.

Chern–Simons vortices in the Gudnason model

Journal of Functional Analysis, 2014

We present a series of existence theorems for multiple vortex solutions in the Gudnason model of the N = 2 supersymmetric field theory where non-Abelian gauge fields are governed by the pure Chern-Simons dynamics at dual levels and realized as the solutions of a system of elliptic equations with exponential nonlinearity over two-dimensional domains. In the full plane situation, our method utilizes a minimization approach, and in the doubly periodic situation, we employ an-inequality constrained minimization approach. In the latter case, we also obtain sufficient conditions under which we show that there exist at least two gauge-distinct solutions for any prescribed distribution of vortices. In other words, there are distinct solutions with identical vortex distribution, energy, and electric and magnetic charges.

Resolution of Chern–Simons–Higgs Vortex Equations

Communications in Mathematical Physics, 2016

It is well known that the presence of multiple constraints of non-Abelian relativisitic Chern-Simons-Higgs vortex equations makes it difficult to develop an existence theory when the underlying Cartan matrix K of the equations is that of a general simple Lie algebra and the strongest result in the literature so far is when the Cartan subalgebra is of dimension 2. In this paper we overcome this difficulty by implicitly resolving the multiple constraints using a degree-theorem argument, utilizing a key positivity property of the inverse of the Cartan matrix deduced in an earlier work of Lusztig and Tits, which enables a process that converts the equality constraints to inequality constraints in the variational formalism. Thus this work establishes a general existence theorem which settles a long-standing open problem in the field regarding the general solvability of the equations.

Remarks on charged vortices in the Maxwell–Chern–Simons model

Physics Letters A, 2003

We study vortex-like configuration in Maxwell-Chern-Simons Electrodynamics. Attention is paid to the similarity it shares with the Nielsen-Olesen solutions at large distances. A magnetic symmetry between a point-like and an azimuthal-like current in this framework is also pointed out. Furthermore, we address the issue of a neutral spinless particle interacting with a charged vortex, and obtain that the Aharonov-Casher-type phase depends upon mass and distance parameters.

Topological charged BPS vortices in Lorentz-violating Maxwell-Higgs electrodynamics

Physical Review D, 2014

We have performed a complete study of BPS vortex solutions in the Abelian sector of the standard model extension (SME). Specifically we have coupled the SME electromagnetism with a Higgs field which is supplemented with a Lorentz-violating CPT-even term. We have verified that Lorentzviolation (LV) belonging to Higgs sector allows to interpolate between some well known models like, Maxwell-Higgs, Chern-Simons-Higgs and Maxwell-Chern-Simons-Higgs. We can also observed that the electrical charged density distribution is nonnull in both CPT-even and CPT-odd models, however the total electric charge in the CPT-even case is null whereas in the CPT-odd one it is proportional to the quantized magnetic flux. The following general results can be established in relation to the LV introduced in the Higgs sector: it changes the vortex Ansatz and the gauge field boundary conditions. The last one is responsible for the magnetic flux besides being proportional to the winding number also depends explicitly in the Lorentz-violation belonging to the Higgs sector.